If it's tripping out when the element turns on, then try running it on the non-GFCI outlet for 15 minutes or so (leave the door open so the element stays on). Then take it back to the GFCI output and see if it stays on. If it does, then your element had just absorbed enough moisture to cause a ground leak (how long since the last time you turned it on?). Annoying, but I don't think it's a big safety problem

If it trips out without the element turning on, then you might have a more permanent ground leakage. It might be grime and oil around AC input to the element, or something between the controller and the element. This might be a genuine safety issue with the case having a path to 120VAC.